In mid-December, we published the 25th anniversary edition of the Royal Statistical Society's Christmas Quiz - a diabolically tough collection of puzzles devised by Dr Tim Paulden. How many did you manage to crack?
(If you would like to take another look at the quiz before seeing the answers, the questions are still available.)
We were delighted to receive a large number of high-quality entries - however, both markers were in agreement that the prizes should be awarded as follows:
First place: Andrew Garratt - who wins a £150 Wiley book voucher and a copy of the board game 'Borel'.
Second place: Paul Southern - who wins a £50 Wiley book voucher and a copy of 'Borel'.
In addition, to mark the 25th anniversary of the RSS Christmas Quiz, the quizmaster will be making a charitable donation of £250, to be split equally between the ten good causes nominated by this year's top-ten entrants (listed below, in alphabetical order). If you have enjoyed the puzzles in this year's quiz, please consider making a small donation to one of these good causes - or another charity close to your heart.
- Alzheimer’s Society (nominated by Michael Pickard)
- Cued Speech UK (nominated by Andrew Garratt)
- GiveWell (nominated by Andy & Sam Knott)
- Great Ormond Street Hospital Children's Charity (nominated by Charles Steinhardt, Paul Melamud, Corey Plover & Eric MV)
- Mind UK (nominated by Leigh Sinton, David Nandi, Steven Barrett, Jake Barrett & Jonny White)
- MND Association (nominated by David Harris)
- RSPCA (nominated by Mark Payton, Gordon Emslie, Merrall Price & Ron Wasserstein)
- Schistosomiasis Control Initiative (nominated by Liam Hughes)
- Sightsavers (nominated by Paul Southern)
- The Forest Foodbank, run by Coleford Baptist Church (nominated by Ian Davies)
And now, the solutions…
Q1. GREETINGS [9 points]
The five strings of initial letters, after correction, come from:
- 'A Visit from St. Nicholas' aka 'The Night Before Christmas' ('Twas the night before Christmas / When all through the house / Not a creature was stirring / Not even a mouse)
- 'We're Walking in the Air' (We're walking in the air / We're floating in the moonlit sky / The people far below are sleeping as we fly / I'm holding very tight / I'm riding in the midnight blue / I'm finding I can fly so high above with you)
- 'Silent Night' (Silent night, holy night / All is calm, all is bright / Round yon virgin, mother and child / Holy infant so tender and mild / Sleep in heavenly peace / Sleep in heavenly peace)
- 'Fairytale of New York' (specifically, verse 3: They've got cars big as bars, they've got rivers of gold / But the wind goes right through you, it's no place for the old / When you first took my hand on a cold Christmas Eve / You promised me Broadway was waiting for me)
- 'A Christmas Carol' (specifically, Scrooge's famous pronouncement: 'I am as light as a feather, I am as happy as an angel, I am as merry as a schoolboy. I am as giddy as a drunken man. A merry Christmas to everybody! A happy New Year to all the world! Hallo here! Whoop! Hallo!')
The fifteen errors, in order, are HIMIWWIAATYYLTM, which are the initial letters of the opening to the song 'Hello' by Adele (Hello / It's me / I was wondering if after all these years you'd like to meet). This song is a particularly apt choice for the first question of the 25th anniversary quiz, as it is the first track from the album '25'. (The song title 'Hello' is also reflected in the question title, 'Greetings'.)
Q2. BILKO [11 points]
All eight individuals have the initials AG:
(a) Art Garfunkel (who performed with Paul Simon as 'Tom & Jerry')
(b) Sir Alec Guinness (who achieved the rank of Lieutenant in World War II, played Colonel Nicholson in 'The Bridge on the River Kwai', and played Obi-Wan 'Ben' Kenobi in the original Star Wars trilogy)
(c) Antony Gormley (who created the sculpture 'Angel of the North', which features in 'Travelling in a Strange Land' by David Park)
(d) Anna Gunn (who famously played Skyler White in Breaking Bad)
(e) Antoine Griezmann (who won the 2018 FIFA World Cup with France while wearing the number 7 shirt, and was also awarded the Silver Boot and Bronze Ball)
(f) Al Gore (who was the 45th Vice President of the USA, four after Nelson Rockefeller)
(g) Amy Grant (born in Augusta, whose golf course hosts the Masters - one of golf's 'majors' - and has an 18th hole called 'Holly')
(h) Ali G (the satirical character created by Sacha Baron Cohen).
Art Garfunkel and Amy Grant have previously collaborated - the context being, appropriately, a Christmas album called 'The Animals' Christmas'. They are labelled (a) and (g) in the above list - another juxtaposition of those two letters.
As many solvers noted, AG is a particularly appropriate choice for the common set of initials because Ag is the chemical symbol for Silver - traditionally associated with a 25th anniversary. Collectively, the eight individuals in this question might therefore be described as 'Silvers' - this explains the question title 'BILKO', since Phil Silvers famously played (Sergeant) Bilko on 'The Phil Silvers Show' (see https://en.wikipedia.org/wiki/The_Phil_Silvers_Show).
Q3. TOM, DICK, AND... [7 points]
The person is 'CBABBAGE' - i.e. Charles Babbage, the world-famous computer pioneer. All of the letters in the message are notes of the musical scale, and the symbols given in the question show how to play these notes on a four-hole ocarina (as hinted at by the word 'blow' in the first sentence). The following diagram (which is available online at the website http://forbiddenislandflutes.com/how-to-play) illustrates this system of notation - and it can be readily seen that the message in the question image corresponds to 'CBABBAGE'.
Charles Babbage is also a celebrated figure of the steampunk genre, which explains the distinctive styling of the image.
The (statistical) significance of the question title 'TOM, DICK, AND...' is that Babbage was one of the founding members of the (Royal) Statistical Society, alongside Thomas Malthus and Richard Jones.
Babbage's close associate Ada Lovelace famously wrote technical notes entitled 'Note A', 'Note B', ..., 'Note G', whose names mirror the seven notes of the musical scale. Following the system of notation shown in the diagram above, her first name - ADA - would be encoded as three similar 2x2 symbols in which the following circles are darkened: [bottom-left]; [top-left + bottom-left + bottom-right]; [bottom-left].
Q4. FLIP THE QUESTION [7 points]
(a) Each of the five acts has a song named after a playing card, but four of them are Queens, while the other is an Ace: 'Queen of Clubs' (KC & The Sunshine Band), 'Queen of Diamonds' (Tom Odell), 'Queen of Spades' (Styx), 'Queen of Hearts' (Dave Edmunds), and 'Ace of Spades' (Motörhead), When 'played together' (as a poker hand of four Queens plus an Ace kicker), the odd one out is the Ace - i.e. Motörhead. This theme is hinted at by the title, since flipping the question ('Q4') gives '4Q' - i.e. four Queens.
(b) By combining carefully-chosen song titles from the fifteen acts, in the order listed, we can recreate (almost all of) the opening lyrics to 'Bohemian Rhapsody' by Queen. (The opening to the song's music video famously features the faces of the four Queen band members - continuing the '4Q' theme.) The fifteen song titles are (in sequence): 'Is This The Real Life' / 'Fantasy' / 'Landslide' / 'Escape from Reality' / 'Open Your Eyes' / 'Look Up to the Sky' / 'Poor Boy' / 'No Sympathy' / 'Because' / 'Easy Come, Easy Go' / 'A Little High' / 'Low' / 'Anyway' / 'The Winds Blows' / 'Don't Matter to Me'.
Q5. LOUD AND CLEAR [5 points]
The feat in question is an NBA '5×5' (or 'five-by-five'), defined as a performance in which a basketball player accumulates at least five points, five rebounds, five assists, five steals, and five blocks in a single game. The initials given in the list denote the following basketball players: JE = Julius Erving, GJ = George T Johnson, GG = George Gervin, DR = David Robinson, DC = Derrick Coleman, VD = Vlade Divac, JT = Jamaal Tinsley, AK = Andrei Kirilenko, MC = Marcus Camby, NB = Nicolas Batum, DG = Draymond Green, and AD = Anthony Davis. (For further details, please see https://nbahoopsonline.com/History/Records/5x5.html and https://en.wikipedia.org/wiki/Five-by-five_(basketball), which provide the tables from which the list of initials was created.)
The person missing from the list is of course Hakeem Olajuwon - the most prolific achiever of 5×5s in NBA history. When his initials are added back into the list (including repeats), the festive message 'HO, HO, HO' is spelled out twice, as illustrated below:
JE, GJ, GG, JE, HO, HO, HO, DR, DC, HO, HO, HO, VD, JT, AK, AK, MC, AK, NB, DG, AD
(Two quick remarks: First, in keeping with the presentation on nbahoopsonline.com, Julius Erving's 5×5 for the New York Nets in 1976 has been retained as the first element of the list, even though this technically falls under the jurisdiction of the American Basketball Association (ABA) rather than the NBA. Second, although the list finishes with the 5×5 achieved by Anthony Davis on 21 November 2018, the Wikipedia page cited above notes that another 5×5 was recently achieved by Jusuf Nurkić on 1 January 2019 - a few weeks after the quiz was released.)
In addition to its basketball usage, the terminology '5×5' also denotes a radio signal that has excellent strength and perfect clarity - this explains the question title, 'LOUD AND CLEAR'. Moreover, as several solvers highlighted, it is particularly apt for the 25th anniversary quiz to feature a question on those who have achieved a '5×5' - and it is also fitting that this is question number 5 in the quiz, and worth 5 points.
Q6. FREEZE-FRAMES [10 points]
Proceeding row by row, from left to right, the images depict the following works:
- 'As the Old Sing, So the Young Pipe' by Jacob JORDAENS
- 'At the Piano' by Louise ABBÉMA
- 'The Tea', also known as 'Five O'Clock Tea', by Mary CASSATT
- 'Sleigh Ride' by Rudolf KOLLER
- '"How Long Has He Been Lost?" Enquired the Giant' (one of several illustrations for 'Johnny and the Giant' in 'St Nicholas Illustrated' magazine) by James Montgomery FLAGG
- 'Nantucket' by Theodore ROBINSON
- 'Dublin Streets: A Vendor of Books' by Walter OSBORNE
- 'Dancing Shoes' by Helene SCHJERFBECK
- 'Snow in the Wood' by Tom THOMSON
The nine surnames, taken in order, spell out the wintry character JACK FROST (which echoes the question title, FREEZE-FRAMES).
Q7. LOTS ON THEIR PLATE [5 points]
(a) The answer is Dun Che Lao Ren - the name of Father Christmas in China. (Dun is a horse of a certain hue, Che [Guevara] is a famous revolutionary, Lao is the official language of Laos, and Ren is the chihuahua from The Ren & Stimpy Show.) To explain the hint (80% of Q2): the theme of Question 2 was 'Silver' and its association with the 25th anniversary, while 'China' is traditionally given for the 20th anniversary. (The word 'plate' in the question title offers a further clue to this theme - and, as several entrants noted, the 'Father Christmas' in the world's most populated country would certainly have 'lots on their plate'.)
(b) Echoing the name of the much-loathed Christmas vegetable (and as hinted at by the question title), Chantal and Isala are playing a game of 'Sprouts' over in Brussels. Sprouts is a paper-and-pencil game invented in the 1960s by Cambridge mathematicians John H Conway and Michael S Paterson - and in fact, Chantal and Isala's moves recreate exactly the example given on the game's Wikipedia page: https://en.wikipedia.org/wiki/Sprouts_(game). Isala smiles after playing her second move because she has won the game. The players' names are references to Chantal Akerman and Isala Van Diest - two famous Belgian women who will soon have streets in Brussels named after them, as announced in summer 2018 (see www.theguardian.com/cities/2018/aug/22/ceci-nest-pas-une-rue-where-the-streets-have-new-names-brussels.)
Q8. THREE POINT FIVE POINT… [3 points]
Versions 3.5.0, 3.5.1 and 3.5.2 (echoing the question title) of the R statistical programming language were released during 2018 - and in keeping with tradition, each had a short codename referencing a historical Peanuts comic strip. Version 3.5.0 was named 'Joy in Playing' (referencing the 27 January 1973 strip), Version 3.5.1 was named 'Feather Spray' (referencing the 9 March 1972 strip), and Version 3.5.2 was named 'Eggshell Igloo' (referencing the 25-26 January 1960 strips). These phrases are visible at the top of the R Console whenever it is opened.
For further details on the connections between R's version names and the Peanuts comic strips, please see the excellent blog post at: https://livefreeordichotomize.com/2017/09/28/r-release-names/.
Q9. SPSS: A SPECIAL ANNIVERSARY [5 points]
Although 2018 was the 50th anniversary year of the SPSS statistical software package, this is a deliberate red herring. In fact, this question concerns an entirely different kind of SPSS: namely, a 'Simple Perfect Squared Square' - and specifically, the order-21 SPSS discovered in 1978 by AJW Duijvestijn, which is shown in the diagram below. (For further background on 'squaring the square', please see http://www.squaring.net/sq/ss/spss/spss.html and https://en.wikipedia.org/wiki/Squaring_the_square.)
As shown in the diagram, the nine numbers on the exterior of Duijvestijn's SPSS (representing the side lengths of the constituent squares) are 50, 35, 27, 19, 24, 42, 37, 33, and 29 - exactly the numbers given in the question. The twelve numbers appearing in the interior are therefore 2, 4, 6, 7, 8, 9, 11, 15, 16, 17, 18, and 25 (listed in order of size).
The largest interior number (25) and three of its neighbours (4, 9, and 16) are all square numbers themselves - a very appropriate property for a question about squared squares. Moreover, as some solvers noted, it is also apt that this is a square-numbered question (namely, question 9) in a quiz that is itself celebrating a square-numbered anniversary (namely, the 25th).
Finally, to receive full credit, solvers should have explained the question title by noting that 2018 was a special anniversary year (namely, the 40th anniversary) for Duijvestijn's SPSS too.
Q10. BICHHOO (YO!) [8 points]
Most entrants correctly deduced that the ten different letters within the word equations needed to be assigned a different digit such that all five results on the right-hand side corresponded to English words. (These ten letters can be rearranged to give the word HYPERBOLIC, a piece of mathematical terminology that is also the name of a probability distribution - a fitting choice for an RSS Quiz.)
Although the number of possible ways to associate the ten letters with the ten digits is very large (3628800 = 10!, where the exclamation mark denotes 'factorial'), the problem can be simplified greatly by realising that the title 'BICHHOO (YO!)' is simply an encoded version of this number of possibilities, i.e. '3628800 (10!)'. Therefore, B=3, I=6, C=2, H=8, O=0, and Y=1. It can then quickly be ascertained from the equations themselves that the code should be completed by setting E=4, L=5, P=7, and R=9 - and the five words on the right-hand side are therefore COPIER, BICYCLE, PYRRHIC, HORROR and EERIER.
The shade of grey appearing in the image's border has a hexadecimal colour code of #808080, which corresponds to the festive message 'HO HO HO' under the encoding used in the question. (Of course, this echoes Q5, where the same message made an appearance.)
'Bichhoo' is the Hindi word for 'Scorpion', so the question title 'BICHHOO (YO!)' would strike a chord with the rapper Drake from Q4, who released a double album called Scorpion in 2018 (which, appropriately, comprised 25 tracks - one of them being 'Don't Matter to Me'). He might even be tempted to add the 'YO!' at the end for emphasis. Drake's full name is Aubrey Drake Graham, so he'd feel particularly at home in Q2, which features famous people with the initials AG.
Q11. P.I.G. [5 points]
The property described in the question is satisfied by the prime numbers in German (and the initials in the question title - 'P.I.G.' - stand for 'Primes In German').
The first 25 primes in German are 'zwei' (2), 'drei' (3), 'fünf' (5), 'sieben' (7), 'elf' (11), and so on, through to 'siebenundneunzig' (97) - and the initial letters of these 25 names follow the letter distribution stated in the question. (Since the German names for the numbers between 20 and 99 always state the units first, followed by the tens, the primes in this range all have names starting with 'ein', 'drei', 'sieben', or 'neun', which explains the high frequencies for the letters 'e', 'd', 's' and 'n'.)
The next 25 elements in the sequence - i.e. the 26th prime through to the 50th prime - range from 'einhunderteins' (101) to 'zweihundertneunundzwanzig' (229). In each case, the number of hundreds is written first, and so it is easy to check that these elements comprise 21 'e's and 4 'z's. (The prefix 'einhundert-' can also be shortened to 'hundert-', so stating the answer as 21 'h's and 4 'z's would also be perfectly correct.)
Finally, the fifth element of the sequence (and the shortest, with only three letters) is 'elf'. Of course, the reason this element 'might provide a little help' is that the elves are known as 'Santa's little helpers'.
Q12. IT'S A LAP [6 points]
The ratio of the longest strand length (orange) to the shortest strand length (purple) is equal to the square root of 21 (or sqrt(21), for brevity). If we take the purple strand to be 1 unit in length, the other coloured strands have the following lengths: green = 2, yellow = sqrt(3), pink = sqrt(7), red = sqrt(13), blue = sqrt(19), and orange = sqrt(21).
Several entrants reached the correct answer by identifying the parallelograms in the figure, and repeatedly applying the well-known formula linking the lengths of a parallelogram's sides to the lengths of its diagonals. However, it turns out that all eight nodes (i.e. tinsel attachment points) in the original diagram lie on a regular triangular grid whose side length equals the length of the purple strand (or equivalently, half of the green strand), as shown in the augmented diagram below. From this augmented diagram, it is easy to calculate the length of each strand colour by applying Pythagoras' Theorem - and the answer of sqrt(21) then follows immediately.
Structures like this - with the special property that each inter-node length occurs a different number of times - are called 'crescent configurations', hence the question's reference to a 'moonlit' night. The particular eight-node crescent configuration illustrated in this question was discovered by Palasti, whose name is revealed by reversing the question title. (Coincidentally, the name 'Palasti' is also an anagram of the word 'spatial'.)
Please see https://www.emis.de/journals/INTEGERS/papers/q38/q38.pdf for further background on crescent configurations (and note that Figure 1 on Page 3 is a rotated version of the original diagram given in the question).
Q13. FUSION [8 points]
(a) When completed, the diagram represents the five different versions of the film 'A Star Is Born' (as hinted at by the title - 'FUSION' - which is the process underlying the birth of stars). The numbers on the arrows indicate the time gap in years between the respective versions, and the pairs of initials indicate the female and male leads. Thus, the first pair JG + FM represents Janet Gaynor and Fredric March (from the original 1937 version); the second pair is JG + JM, representing Judy Garland and James Mason (from the 1954 version, 17 years later); the third pair is BS + KK, representing Barbra Streisand and Kris Kristofferson (from the 1976 version); the fourth pair is SK + ARK, representing Shraddha Kapoor and Aditya Roy Kapur (from the 2013 Bollywood version); and the fifth and final pair, LG + BC, represents Lady Gaga and Bradley Cooper (from the 2018 version). Lady Gaga is linked to theme of Q4 in two different ways: she wrote the iconic dance-pop song 'Poker Face' (echoing the poker hand theme in Q4a), and the name 'Lady Gaga' was originally derived from the song 'Radio Ga Ga' by the rock group Queen (echoing Q4b).
(b) Continuing the themes of 'a star is born' and 'fusion', part (b) concerns the different configurations of stars appearing on the flag of the United States of America during the evolution of 'the union' - and specifically, the five configurations that have been adopted for the greatest length of time. The left-hand side of each 'equation' indicates a particular configuration of stars (e.g. 4 × 6 means 4 rows of 6), while the right-hand side indicates the number of years for which that configuration was in use, according to Wikipedia (see https://en.wikipedia.org/wiki/Flag_of_the_United_States). The missing entry in the final row should therefore be filled in with 5 × 6 + 4 × 5 (i.e. the current configuration of 50 stars), which has been in use for 58 years. Finally, it is apt that this is question number 13, as this has been the number of stripes on the American flag throughout the course of its evolution (with the exception of the 23 year period between 1 May 1795 and 3 July 1818).
Q14. HEX 19 [6 points]
Using computer simulations, spreadsheet calculations, or just a healthy dose of intuition, many entrants correctly assessed that Nathaniel's stroll was most likely to finish in the second hex down in the column one to the right of his starting hex. (This hex is only two steps away from Nathaniel's starting hex, and has a full complement of six neighbours.)
The question title 'HEX 19' is a coded reference to DEC 25 (i.e. Christmas), since the hexadecimal number '19' is equal to the decimal number '25' - and, as several entrants noted, the island depicted in the question is Christmas Island.
A handful of entrants also noted that the 'Silver' theme from Q2 also resurfaces with a vengeance: 'Nathaniel' is the famous statistician Nate Silver; his stroll begins at Silver City (located in the indicated region of Christmas Island); and 'after a barbecue' is a nod to Long John Silver from Treasure Island, whose nickname was 'Barbecue'. Many congratulations if you managed to spot all of these cryptic connections.
Q15. THE BROMPTONS [5 points]
Philip's advent calendar has the special property that each row represents a square number, if we concatenate the five numbered doors from left to right - for instance, the top row contains the number 1218816 which equals 1104 squared, the next row contains 231192025 which equals 15205 squared, and so on. A helpful clue is provided by the question title, since 'The Bromptons' is a London address on Rose Square (a pun on 'rows square') - moreover, it is the former site of Brompton Hospital, whose establishment in the 1840s was spearheaded by Sir Philip Rose, mirroring the 'Philip' in the question. (See the webpage http://www.thebromptons.org.uk/?c=4154 for further details.)
Finally, as several entrants noted, the calendar also contains a bonus festive message: under the standard letters-to-numbers mapping (whereby A=1, B=2, C=3, and so on), the five doors in the central column of the calendar spell out 'RINGS' in gold - i.e. 'five gold rings'.
The 25th Anniversary Edition of the Royal Statistical Society Christmas Quiz was set by Dr Tim Paulden. Many thanks to Jon Nelson and Tom Thorpe for their helpful contributions.